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Learn · Numeracy · 4 min

Ratios, from scratch

A ratio compares quantities — how much of one thing there is for another:

See it: a ratio compares two amounts

2 blue3 yellow

Ratio 2 : 3 ·  5 parts in total

“2 to 3” means for every 2 blue there are 3 yellow. Order matters.

Now — sharing in a ratio

Share 20 lollies between two kids in the ratio 2 : 3. Work in parts.

The one move: find one part first

  • ① Total parts = 2 + 3 = 5
  • ② One part = 20 ÷ 5 = 4 lollies
  • ③ Shares = 2 × 4 and 3 × 4 = 8 and 12
  • Check: 8 + 12 = 20 ✓

Handy trick — write the parts as 2n and 3n

Every “part” is the same size — call it n. So a 2 : 3 split is just 2n and 3n. Add them, solve for n, then read off each amount.

  • 20 students, boys : girls = 2 : 3
  • ① 2n + 3n = 20 → 5n = 20 → n = 4
  • ② Boys = 2n = 8  ·  Girls = 3n = 12
  • Check: 8 + 12 = 20 ✓

Tips & tricks

Simplify — divide both sides by the same number
4 : 6 = 2 : 3 (both ÷ 2)
Share an amount — total parts → one part → multiply
Share 30 in 1 : 4 → 5 parts → 30 ÷ 5 = 6 → 6 and 24
Ratio ↔ fraction
In 2 : 3, the blue is 25 of the whole (2 out of 5 parts)
Given ONE amount, find the rest
2 : 3 and there are 8 boys (the “2”)? One part = 8 ÷ 2 = 4, so girls = 3 × 4 = 12.

Now you try — 0/3

1. Simplify the ratio 6 : 9.

2. Share 20 in the ratio 2 : 3. How big is the LARGER share?

3. In the ratio 3 : 1, what fraction of the whole is the first part?

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